Investigatory Project in Physics (S.Y. 2010-2011)

Joule’s Apparatus Model

Michiko Reyes Reyna Regine Tarnate

Maxene Mae Go Patricia Ocso

Leeanne Sandra Camposano Brayn Aldrich Albio

IV-Meekness

Tchr. Merlyn V. Cortes

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James Prescott Joule was an English physicist and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work. This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The SI derived unit of energy, the joule, is named after him. He worked with Lord Kelvin to develop the absolute scale of temperature, made observations on magnetostriction, and found the relationship between the current through a resistance and the heat dissipated, now called Joule's law according to Wikipedia.

One of his discoveries was the mechanical equivalent of heat. He created an apparatus called “Joule’s apparatus” wherein he was able to demonstrate the conversion of work into heat or simply called as mechanical equivalent of heat. In his apparatus, he used an insulated container with paddles connected to weights that stirred water inside it. Stationary vanes broke up the flow so the work done by the weights is not purely converted into kinetic energy. The potential energy lost by the weights produced an increase in temperature by one degree Fahrenheit per one pound of water by the use of 772 ft-lb of work.

The mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century. The concept stated that motion and heat are mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, provided the work done is totally converted to heat energy. His apparatus showed that there was an actual number relating mechanical work to heat, which is a major idea, thus why the unit of energy is named after him.The contraption he made was "a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy (heat) gained by the water by friction with the paddle."

And so we have thought of creating a model of Joule’s apparatus so that people would understand how does this apparatus functions of converting work into heat. This could be of help for Physics teacher in teaching this principle in class, to easily demonstrate the conversion of work into energy.

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This study aims to develop a model of Joule’s apparatus to show the principle of mechanical equivalent of heat. This study specifically aims to:

1. Elaborate the principle of Joule’s apparatus. 2. State the process of this apparatus. 3. Make a model of Joule’s apparatus to help Physics teachers in discussing this

principle.

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Our group intends to create a model of Joule’s apparatus. This can benefit the Physics teachers, students and some researchers as well. This model would help the Physics teachers in discussing the principle of mechanical equivalent of heat that will ease the students in understanding this principle.

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This study is delimited to the procedure of making this model, the materials used, the principles behind this apparatus and the function of this model of Joule’s apparatus. This study involves the student and teachers of National Christian Life College during this school year 2010-2011 at National Christian Life College Marikina Chapter. This specially involves the fourth year students who study physics.

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1. Work-In physics, mechanical work is the amount of energy transferred by a force

acting through a distance. 2. Heat-it is an energy transfer to the body in any other way than due to work

performed on the body. 3. Kinetic Energy-It is defined as the work needed to accelerate a body of a given

mass from rest to its stated velocity. 4. Potential Energy-is the energy stored in a body or in a system due to its position

in a force field or due to its configuration. 5. Conversion-a change in form 6. Thermodynamics-is the science of energy conversion involving heat and other

forms of energy, most notably mechanical work. 7. Apparatus-a device that is used for a specific purpose 8. Model-a physical representation of an object

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James Prescott Joule

James Prescott Joule FRS (pronounced /ˈdʒuːl/; 24 December 1818 – 11 October 1889) was an English physicist and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The SI derived unit of energy, the joule, is named after him. He worked with Lord Kelvin to develop the absolute scale of temperature, made observations on magnetostriction, and found the relationship between the current through a resistance and the heat dissipated, now called Joule's law.

The mechanical equivalent of heat

Joule wrote in his 1845 paper:

... the mechanical power exerted in turning a magneto-electric machine is converted into the heat evolved by the passage of the currents of induction through its coils; and, on the other hand, that the motive power of the electro-magnetic engine is obtained at the expense of the heat due to the chemical reactions of the battery by which it is worked.

Joule's Heat Apparatus, 1845

Joule here adopts the language of vis viva (energy), possibly because Hodgkinson had read a review of Ewart's On the measure of moving force to the Literary and Philosophical Society in April 1844.

Further experiments and measurements by Joule led him to estimate the mechanical equivalent of heat as 838 ft·lbf of work to raise the temperature of a pound of water by one degree Fahrenheit. He announced his results at a meeting of the chemical section of the British Association for the Advancement of Science in Cork in 1843 and was met by silence.

Joule was undaunted and started to seek a purely mechanical demonstration of the conversion of work into heat. By forcing water through a perforated cylinder, he was able to measure the slight viscous heating of the fluid. He obtained a mechanical equivalent of 770 ft·lbf/Btu (4.14 J/cal). The fact that the values obtained both by electrical and purely mechanical means were in agreement to at least one order of magnitude was, to Joule, compelling evidence of the reality of the convertibility of work into heat.

Joule now tried a third route. He measured the heat generated against the work done in compressing a gas. He obtained a mechanical equivalent of 823 ft·lbf/Btu (4.43 J/cal). In many ways, this experiment offered the easiest target for Joule's critics but Joule disposed of the anticipated objections by clever experimentation. However, his paper was rejected by the Royal Society and he had to be content with publishing in the Philosophical Magazine. In the paper he was forthright in his rejection of the caloric reasoning of Carnot and Émile Clapeyron, but his theological motivations also became evident:

I conceive that this theory ... is opposed to the recognised principles of philosophy because it leads to the conclusion that vis viva may be destroyed by an improper disposition of the apparatus: Thus Mr Clapeyron draws the inference that 'the temperature of the fire being 1000°C to 2000°C higher than that of the boiler there is an enormous loss of vis viva in the passage of the heat from the furnace to the boiler.' Believing that the power to destroy belongs to the Creator alone I affirm ... that any theory which, when carried out, demands the annihilation of force, is necessarily erroneous.

In 1845, Joule read his paper On the mechanical equivalent of heat to the British Association meeting in Cambridge. In this work, he reported his best-known experiment, involving the use of a falling weight to spin a paddle-wheel in an insulated barrel of water, whose increased temperature he measured. He now estimated a mechanical equivalent of 819 ft·lbf/Btu (4.41 J/cal).

In 1850, Joule published a refined measurement of 772.692 ft·lbf/Btu (4.159 J/cal), closer to twentieth century estimates.

Reception and priority

Joule's apparatus for measuring the mechanical equivalent of heat

Much of the initial resistance to Joule's work stemmed from its dependence upon extremely precise measurements. He claimed to be able to measure temperatures to within 1/200 of a degree Fahrenheit. Such precision was certainly uncommon in contemporary experimental physics but his doubters may have neglected his experience in the art of brewing and his access to its practical technologies. He was also ably supported by scientific instrument-maker John Benjamin Dancer.

However, in Germany, Hermann Helmholtz became aware both of Joule's work and the similar 1842 work of Julius Robert von Mayer. Though both men had been neglected since their respective publications, Helmholtz's definitive 1847 declaration of the conservation of energy credited them both.

Also in 1847, another of Joule's presentations at the British Association in Oxford was attended by George Gabriel Stokes, Michael Faraday, and the precocious and maverick William Thomson, later to become Lord Kelvin, who had just been appointed professor of natural philosophy at the University of Glasgow. Stokes was "inclined to be a Joulite" and Faraday was "much struck with it" though he harboured doubts. Thomson was intrigued but skeptical.

Unanticipated, Thomson and Joule met later that year in Chamonix. Joule married Amelia Grimes on 18 August and the couple went on honeymoon. Marital enthusiasm notwithstanding, Joule and Thomson arranged to attempt an experiment a few days later to measure the temperature difference between the top and bottom of the Cascade de Sallanches waterfall, though this subsequently proved impractical.

Though Thomson felt that Joule's results demanded theoretical explanation, he retreated into a spirited defense of the Carnot-Clapeyron school. In his 1848 account of absolute temperature, Thomson wrote that "the conversion of heat (or caloric) into mechanical effect is probably impossible, certainly undiscovered"- but a footnote signaled his first doubts about the caloric theory, referring to Joule's "very remarkable discoveries". Surprisingly, Thomson did not send Joule a copy of his paper but when

Joule eventually read it he wrote to Thomson on 6 October, claiming that his studies had demonstrated conversion of heat into work but that he was planning further experiments. Thomson replied on the 27th, revealing that he was planning his own experiments and hoping for a reconciliation of their two views. Though Thomson conducted no new experiments, over the next two years he became increasingly dissatisfied with Carnot's theory and convinced of Joule's. In his 1851 paper, Thomson was willing to go no further than a compromise and declared "the whole theory of the motive power of heat is founded on ... two ... propositions, due respectively to Joule, and to Carnot and Clausius".

As soon as Joule read the paper he wrote to Thomson with his comments and questions. Thus began a fruitful, though largely epistolary, collaboration between the two men, Joule conducting experiments, Thomson analysing the results and suggesting further experiments. The collaboration lasted from 1852 to 1856, its discoveries including the Joule-Thomson effect, and the published results did much to bring about general acceptance of Joule's work and the kinetic theory.

James Prescott Joule's Contribution

James Prescott Joule (1818 – 1889), an English physicist, calculated in 1843, a few decades after Rumford’s cannon experiments, the mechanical equivalent of heat in a series of experiments. In the most famous apparatus he built for this end, now called the Joule apparatus (see image below), a descending weight attached to a string caused a paddle immersed in water to rotate and heat the water. Joule supposed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy (heat) gained by the water by friction with the paddle.

In this experiment, the friction and agitation by the paddle-wheel of the body of water, trapped in an insulated barrel, caused heat to be generated which, in turn, increased the temperature of the water. The temperature change ∆T of the water and the height of the fall ∆h of the weight m*g were recorded. Using these values, Joule was able to determine the mechanical equivalent of heat.

Specifically, Joule had experimented on the amount of mechanical work generated by friction needed to raise the temperature of a pound of water by one degree Fahrenheit and found a consistent value of 772.24 foot pound force (in English units) or 4.1550 J/cal (SI metric units) in comparison to the 4.1868 J/cal modern value – meaning that around 4.2 J were needed to raise the temperature of 1g of water by 1°.C - and that’s the mechanical equivalent of heat in its respective units (The Joule unit was introduced after Joule's times (after him) and he calculated the mechanical equivalent of heat in English units).

Joule contended that motion and heat were mutually interchangeable and that, in every case, a given amount of work (motion) would generate the same amount of heat. Moreover, he also claimed that heat was only one of many forms of energy (electrical, mechanical, chemical) and only the sum of all forms was conserved. Otherwise the calculated mechanical equivalent of heat is meaningless.

In 1845, James Joule reported his experiment in a paper On the mechanical equivalent of heat for the British Association meeting in Cambridge.

Heat

In physics and thermodynamics, heat is energy transferred from one place in a body or thermodynamic system to another place, or beyond the boundary of one system to another one due to thermal contact even when the systems are at different temperatures. It is also often described as the process of transfer of energy between physical entities. In this description, it is an energy transfer to the body in any other way than due to work performed on the body.

In engineering, the discipline of heat transfer classifies energy transfer in or between systems resulting in the change of thermal energy of a system as either thermal conduction, first described scientifically by Joseph Fourier, by fluid convection, which is the mixing of hot and cold fluid regions due to pressure differentials, by mass transfer, and by thermal radiation, the transmission of electromagnetic radiation described by black body theory.

Thermodynamically, energy can only be transferred by heat between objects, or regions within an object, with different temperatures, a consequence of the zeroth law of thermodynamics. This transfer happens spontaneously only in the direction to the colder body, as per the second law of thermodynamics. The transfer of energy by heat from one object to another object with an equal or higher temperature can happen only with the aid of a heat pump via mechanical work.

A related term is thermal energy, loosely defined as the energy of a body that increases with its temperature. Heat is also often referred to as thermal energy, although many definitions require this thermal energy to be in transfer between two systems to be called heat, otherwise, many sources prefer to continue to refer to the internal quantity as thermal energy.

Overview

Heat flows spontaneously from systems of higher temperature to systems of lower temperature, but heat flow in the opposite direction is not spontaneous. When two

systems of different temperatures come into thermal contact, they exchange thermal energy, i.e. heat, but the hotter body gives to the colder body more thermal energy than it takes from it, until their temperatures are equal, which at that point they obtain a state of thermal equilibrium.

The first law of thermodynamics states that the energy of an isolated system is conserved. Therefore, to change the energy of a system, energy must be transferred to or from the system. Heat and work are the only two mechanisms by which energy can be transferred. Work performed on a system is, by definition, an energy transfer to the system that is due to a change to external parameters of the system, such as the volume, magnetization, center of mass in a gravitational field. Heat is the energy transferred to the system in any other way.

In the case of systems close to thermal equilibrium where notions such as the temperature can be defined, heat transfer can be related to temperature difference between systems. It is an irreversible process that leads to the systems coming closer to mutual thermal equilibrium.

Human notions such as hot and cold are relative terms and are generally used to compare one system’s temperature to another or its surroundings.

Definitions

Scottish physicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of the first to enunciate a modern definition of heat. Maxwell outlined four stipulations for the definition of heat:

• It is something which may be transferred from to another, according to the second law of thermodynamics.

• It is a measurable quantity, and thus treated mathematically. • It cannot be treated as a substance, because it may be transformed into

something that is not a substance, e.g., mechanical work. • It is one of the forms of energy.

Several modern definitions of heat are as follows:

• The energy transferred from a high-temperature system to a lower-temperature system is called heat.

• Any spontaneous flow of energy from one system to another caused by a difference in temperature between the systems is called heat.

• In a thermodynamic sense, heat is never regarded as being stored within a system. Like work, it exists only as energy in transit from one system to another or between a system and its surroundings. When energy in the form of heat is added to a system, it is stored as kinetic and potential energy of the atoms and molecules in the system.

Notation and units

As a form of energy heat has the unit joule (J) in the International System of Units (SI). However, in many applied fields in engineering the British Thermal Unit (BTU) and the calorie are often used. The standard unit for the rate of heat transferred is the watt (W), defined as joules per second.

The total amount of energy transferred as heat is conventionally written as Q for algebraic purposes. Heat released by a system into its surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat from its surroundings, it is positive (Q > 0). Heat transfer rate, or heat flow per unit time, is denoted by

.

Heat flux is defined as rate of heat transfer per unit cross-sectional area, resulting in the unit watts per square metre.

Entropy

In 1856, German physicist Rudolf Clausius defined the second fundamental theorem (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): "if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat Q from work at the temperature T, has the equivalence-value:"

In 1865, he came to define this ratio as entropy symbolized by S, such that, for a closed, stationary system:

and thus, by reduction, quantities of heat δQ (an inexact differential) are defined as quantities of TdS (an exact differential):

In other words, the entropy function S facilitates the quantification and measurement of heat flow through a thermodynamic boundary.

To be precise, this equality is only valid, if the heat δQ is applied reversibly. If, in contrast, irreversible processes are involved, e.g. some sort of friction, then instead of the above equation one has

This is the second law of thermodynamics.

Conservation of energy

The law of conservation of energy is an empirical law of physics. It states that the total amount of energy in an isolated system remains constant over time (is said to be conserved over time). A consequence of this law is that energy can neither be created or destroyed: it can only be transformed from one state to another. The only thing that can happen to energy in a closed system is that it can change form: for instance chemical energy can become kinetic energy.

Albert Einstein's theory of relativity shows that energy and mass are the same thing, and that neither one appears without the other. Thus in closed systems, both mass and energy are conserved separately, just as was understood in pre-relativistic physics. The new feature of relativistic physics is that "matter" particles (such as those constituting atoms) could be converted to non-matter forms of energy, such as light; or kinetic and potential energy (example: heat). However, this conversion does not affect the total mass of systems, because the latter forms of non-matter energy still retain their mass through any such conversion.

Today, conservation of “energy” refers to the conservation of the total system energy over time. This energy includes the energy associated with the rest mass of particles and all other forms of energy in the system. In addition, the invariant mass of systems of particles (the mass of the system as seen in its center of mass inertial frame, such as the frame in which it would need to be weighed) is also conserved over time for any single observer, and (unlike the total energy) is the same value for all observers. Therefore, in an isolated system, although matter (particles with rest mass) and "pure energy" (heat and light) can be converted to one another, both the total amount of energy and the total amount of mass of such systems remain constant over time, as seen by any single observer. If energy in any form is allowed to escape such systems (see binding energy), the mass of the system will decrease in correspondence with the loss.

A consequence of the law of energy conservation is that perpetual motion machines can only work perpetually if they deliver no energy to their surroundings.

Mechanical equivalent of heat

A key stage in the development of the modern conservation principle was the demonstration of the mechanical equivalent of heat. The caloric theory maintained that heat could neither be created nor destroyed but conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.

In 1798 Count Rumford (Benjamin Thompson) performs measurements of the frictional heat generated in boring cannons and develops the idea that heat is a form of kinetic energy; his measurements refute caloric theory, but are imprecise enough to leave room for doubt.

The mechanical equivalence principle was first stated in its modern form by the German surgeon Julius Robert von Mayer in 1842. Mayer reached his conclusion on a voyage to the Dutch East Indies, where he found that his patients' blood was a deeper red because they were consuming less oxygen, and therefore less energy, to maintain their body temperature in the hotter climate. He had discovered that heat and mechanical work were both forms of energy, and later, after improving his knowledge of physics, he calculated a quantitative relationship between them (pub' 1845).

Joule's apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate.

Meanwhile, in 1843 James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. In the most famous, now called the "Joule apparatus", a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy (heat) gained by the water by friction with the paddle.

Over the period 1840–1843, similar work was carried out by engineer Ludwig A. Colding though it was little known outside his native Denmark.

Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that, perhaps unjustly, eventually drew the wider recognition.

For the dispute between Joule and Mayer over priority, see Mechanical equivalent of heat: Priority

In 1844, William Robert Grove postulated a relationship between mechanics, heat, light, electricity and magnetism by treating them all as manifestations of a single "force" (energy in modern terms). In 1874 Grove published his theories in his book The Correlation of Physical Forces. In 1847, drawing on the earlier work of Joule, Sadi Carnot and Émile Clapeyron, Hermann von Helmholtz arrived at conclusions similar to Grove's and published his theories in his book Über die Erhaltung der Kraft (On the Conservation of Force, 1847). The general modern acceptance of the principle stems from this publication.

In 1877, Peter Guthrie Tait claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the Philosophiae Naturalis Principia Mathematica. This is now regarded as an example of Whig history.

The first law of thermodynamics

Entropy is a function of a quantity of heat which shows the possibility of conversion of that heat into work.

For a thermodynamic system with a fixed number of particles, the first law of thermodynamics may be stated as:

, or equivalently,

where δQ is the amount of energy added to the system by a heating process, δW is the amount of energy lost by the system due to work done by the system on its surroundings and dU is the change in the internal energy of the system.

The δ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the dU increment of internal energy (see Inexact differential). Work and heat are processes which add or subtract energy, while the internal energy U is a particular form of energy associated with the system. Thus the term "heat energy" for δQ means "that amount of energy added as the result of heating" rather than referring to a particular form of energy. Likewise, the term "work energy" for δW means "that amount of energy lost as the result of work". The most significant result of this distinction is the fact that one can clearly state the amount of internal energy possessed by a thermodynamic system, but one cannot tell how much energy has flowed into or out of the system as a result of its being heated or cooled, nor as the result of work being performed on or by the system. In simple terms, this means that energy cannot be created or destroyed, only converted from one form to another.

For a simple compressible system, the work performed by the system may be written

where P is the pressure and dV is a small change in the volume of the system, each of which are system variables. The heat energy may be written

where T is the temperature and dS is a small change in the entropy of the system. Temperature and entropy are also system variables.

Kinetic energy

The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.

The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference. For example, a bullet passing an observer has kinetic energy in the reference frame of this observer, but the same bullet is stationary, and so has zero kinetic energy, from the point of view of an observer moving with the same velocity as the bullet. By contrast, the total kinetic energy of a system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame, unless all the objects have the same velocity. In any other case the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system's invariant mass, which is independent of the reference frame.

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is mv2/2. In relativistic mechanics, this is only a good approximation when v is much less than the speed of light.

History and etymology

The adjective kinetic has its roots in the Greek word κίνησις (kinesis) meaning motion, which is the same root as in the word cinema, referring to motion pictures.

The principle in classical mechanics that E ∝ mv² was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the living force, vis viva. Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, 's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation.

The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term "kinetic energy" c. 1849–51.

Introduction

Energy occurs in many forms: chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, rest energy. These can be categorized in two main classes: potential energy and kinetic energy.

Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a cyclist uses chemical energy that was provided by food to accelerate a bicycle to a chosen speed. This speed can be maintained without further work, except to overcome air-resistance and friction. The chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist.

The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat.

Like any physical quantity which is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference. Thus, the kinetic energy of an object is not invariant.

Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. This kinetic energy remains constant while in orbit because there is almost no friction in near-earth space. However it becomes apparent at re-entry when some of the kinetic energy is converted to heat.

Kinetic energy can be passed from one object to another. In the game of billiards, the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically and the ball it collided with accelerates to a speed as the kinetic energy is passed on to it. Collisions in billiards are effectively elastic collisions, in which kinetic energy is preserved. In inelastic collisions, kinetic energy is dissipated in various forms of energy, such as heat, sound, binding energy (breaking bound structures).

Flywheels have been developed as a method of energy storage. This illustrates that kinetic energy is also stored in rotational motion.

Several mathematical description of kinetic energy exist that describe it in the appropriate physical situation. For objects and processes in common human experience, the formula ½mv² given by Newtonian (classical) mechanics is suitable. However, if the speed of the object is comparable to the speed of light, relativistic effects become significant and the relativistic formula is used. If the object is on the atomic or sub-atomic scale, quantum mechanical effects are significant and a quantum mechanical model must be employed.

Potential energy

In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule (symbol J). The term "potential energy" was coined by the 19th century Scottish engineer and physicist William Rankine.

Overview

Potential energy exists when a force acts upon an object that tends to restore it to a lower energy configuration. This force is often called a restoring force. For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, unstretched position. Similarly, when a mass is lifted up, the force of gravity will act so as to bring it back down. The action of stretching the spring or lifting the mass requires energy to perform. The energy that went into lifting up the mass is stored in its position in the gravitational field, while similarly, the energy it took to stretch the spring is stored in the metal. According to the law of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. Instead, it is stored as

potential energy. If the spring is released or the mass is dropped, this stored energy will be converted into kinetic energy by the restoring force, which is elasticity in the case of the spring, and gravity in the case of the mass. Think of a roller coaster. When the coaster climbs a hill it has potential energy. At the very top of the hill is its maximum potential energy. When the car speeds down the hill potential energy turns into kinetic. Kinetic energy is greatest at the bottom.

The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position.

There are various types of potential energy, each associated with a particular type of force. More specifically, every conservative force gives rise to potential energy. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their mutual positions.

As a general rule, the work done by a conservative force F will be

where ∆U is the change in the potential energy associated with that particular force. Common notations for potential energy are U, V, Ep, and PE.

Mechanical equivalent of heat

In the history of science, the mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century.

The concept stated that motion and heat are mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, provided the work done is totally converted to heat energy.

History and priority dispute

Joule's apparatus for measuring the mechanical equivalent of heat in which the "work" of the falling weight is converted into the "heat" of agitation in the water.

Count Rumford had observed the frictional heat generated by boring cannon at the arsenal in Munich, Germany circa 1797. Rumford immersed a cannon barrel in water and arranged for a specially blunted boring tool. He showed that the water could be boiled within roughly two and a half hours and that the supply of frictional heat was seemingly inexhaustible. Based on his experiments, he published "An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction", (1798), Philosophical Transaction of the Royal Society p.102. This was the scientific paper by Benjamin Thompson, Count Rumford, that provided a substantial challenge to established theories of heat and began the 19th century revolution in thermodynamics. The experiment inspired the work of James Prescott Joule in the 1840s. Joule's more exact measurements on equivalence were pivotal in establishing the kinetic theory at the expense of the caloric theory. The idea that heat and work are equivalent was also proposed by Julius Robert von Mayer in 1842 in the leading German physics journal and independently by James Prescott Joule in 1843 in the leading British physics journal. Similar work was carried out by Ludwig A. Colding in 1840-1843, though Colding's work was little known outside his native Denmark. A collaboration between Nicolas Clément and Sadi Carnot in the 1820s had some related thinking near the same lines.[1] In 1845 Joule published a paper entitled "The Mechanical Equivalent of Heat", in which he specified a numerical value for the amount of mechanical work required to produce a unit of heat. In particular Joule had experimented on the amount of mechanical work generated by friction needed to raise the temperature of a pound of water by one degree Fahrenheit and found a consistent value of 772.24 foot pound force (4.1550 J·cal-1). Joule contended that motion and heat were mutually interchangeable and that, in every case, a given amount of work would generate the same amount of heat. Von Mayer also published a numerical value for mechanical equivalent of heat in 1845 but his experimental method wasn't as convincing.

Though a standardised value of 4.1860 J·cal-1 was established in the early 20th century, in the 1920s, it was ultimately realised that the constant is simply the specific heat of water, a quantity that varies with temperature between the values of 4.17 and 4.22 J·g-

1·°C-1. The change in unit was the result of the demise of the calorie as a unit in physics and chemistry.

Both von Mayer and Joule met with initial neglect and resistance, despite having published in leading European physics journals. But by 1847 lots of the leading scientists of day were paying attention. Hermann Helmholtz in 1847 published what is considered a definitive declaration of the conservation of energy. Helmholtz had learned from reading Joule's publications, though Helmholtz eventually came around to crediting both Joule and von Mayer for priority.

Also in 1847, Joule made a well-attended presentation at the annual meeting of British Association for the Advancement of Science. Among those in attendance was William Thomson. Thomson was intrigued but initially skeptical. Over the next two years, Thomson became increasingly convinced of Joule's theory, finally admitting his conviction in print in 1851, simultaneously crediting von Mayer. Thomson collaborated with Joule, mainly by correspondence, Joule conducting experiments, Thomson analysing the results and suggesting further experiments. The collaboration lasted from 1852 to 1856. Its published results did much to bring about general acceptance of Joule's work and the kinetic theory.

However, in 1848, von Mayer had first had sight of Joule's papers and wrote to the French Académie des Sciences to assert priority. His letter was published in the Comptes Rendus and Joule was quick to react. Thomson's close relationship with Joule allowed him to become dragged into the controversy. The pair planned that Joule would admit von Mayer's priority for the idea of the mechanical equivalent but to claim that experimental verification rested with Joule. Thomson's associates, co-workers and relatives such as William John Macquorn Rankine, James Thomson, James Clerk Maxwell, and Peter Guthrie Tait joined to champion Joule's cause.

However, in 1862, John Tyndall, in one of his many excursions into popular science and many public disputes with Thomson and his circle, gave a lecture at the Royal Institution entitled On Force[1] in which he credited von Mayer with conceiving and measuring the mechanical equivalent of heat. Thomson and Tait were angered, and an undignified public exchange of correspondence took place in the pages of the Philosophical Magazine, and the rather more popular Good Words. Tait even resorted to championing Colding's cause in an attempt to undermine von Mayer.

Though Tyndall again pressed von Mayer's cause in Heat: A Mode of Motion (1863) with the publication of Sir Henry Enfield Roscoe's Edinburgh Review article Thermo-Dynamics in January 1864, Joule's reputation was sealed while that of von Mayer entered a period of obscurity.

Notes

1. ^ The usage of terms such as work, force, energy, power, etc. in the 18th and 19th centuries by scientific workers does not necessarily reflect the standardised modern usage.

By electrical method Joule's constant,

Where,

V is the applied voltage I is the current passed t is the time (in seconds) m1 is the mass of calorimeter m2 is the mass of water c1 is the specific heat capacity of calorimeter = 0.09 cal / g °C c2 is the specific heat capacity of water = 1 cal / g °C T1 is the initial temperature of water T2 is the final temperature of water

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Experimental Design

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National Christian Life College is a school in a subdivision. And the students are average leveled students. Most of the sources came from the internet and some came from books.

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National Christian Life College is a school in a subdivision. It is an eight-story building.

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The students are average leveled I can say. They study hard.

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1. Empty Used Mayonnaise Plastic Jar with Cover 2. Plastic Vanes (4 pcs.) 3. PVC Pipe ½ (15.5 inches or 0.3937 meters) 4. Arnis Stick (1 pc.) 5. Black Paint 6. Electric Tape 7. Masking Tape 8. Glue Stick 9. Hammer 10. Tape Measure 11. Candle 12. Screw Driver 13. Plaster of Paris (1 kg.) 14. 2 Small Plastic Container 15. Water 16. Paint Brush 17. Match 18. Nail 19. Used Tape Holders 20. Rope 21. Cutter 22. Scissor 23. Old Newspapers 24. Saw

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1. Prepare all the materials and equipment needed first. 2. Measure the PVC pipe then slice it into 15.5 inches. Set aside after. 3. Prepare the 4 pieces of plastic vanes. 4. Cut the PVC pipe into four sections then insert the 4 pieces of plastic vanes into

those four sections. Set aside

5. Get the arnis stick and slice it to 7 inches. 6. Insert the arnis stick into the PVC pipe’s hole. Do not totally insert the whole

stick, just the end part of it. 7. Cover both of it all over with electrical tape. Set aside. 8. Get empty mayonnaise plastic jar and open the lid. 9. Estimate the measurement of the width of the tube then trace it to the center of

the cover. 10. Remove the traced part. 11. Then thicken the part where the hole is at the end with masking tape then

painting it with black paint. 12. Cut two sticks with the same length of at least 3 inches then stick the two of it

that would look like this …

13. Then glue it to the main stick so it would look like this …

14. Set aside. Now paint the jar with black paint. Let it dry. 15. Put the main tube inside the jar. Set aside. 16. Fill the two empty plastic containers with plaster of Paris and pour in hot water.

Let it dry. 17. Put rope on the two containers. 18. Now slice again 2 pieces of stick of the same length about 5 inches or more.

Cover it also with electric tape.

19. Now, roll the rope on the used tape containers at least 2 rounds then paste it using glue stick then glue the stick inside the tape holder pressing the rope under. Let it dry. Do it at the same with the other one.

20. Now set it up. It’s done!

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This section will now talk about the principle of the apparatus created.

In the history of science, the mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century.

The concept stated that motion and heat are mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, provided the work done is totally converted to heat energy.

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To show the structure of the Apparatus. Stir the water inside it with weights and the work produced would be converted into heat.

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I therefore conclude that this model models Joule’s apparatus of Mechanical Equivalent of Heat is an effective tool to teach students about this principle. The next researcher may improve our product when it comes to the structure of the apparatus.